Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, x\neq 0$. $\dfrac{{(p^{5})^{5}}}{{(p^{5}x)^{2}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{5}}$ to the exponent ${5}$ . Now ${5 \times 5 = 25}$ , so ${(p^{5})^{5} = p^{25}}$ In the denominator, we can use the distributive property of exponents. ${(p^{5}x)^{2} = (p^{5})^{2}(x)^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{5})^{5}}}{{(p^{5}x)^{2}}} = \dfrac{{p^{25}}}{{p^{10}x^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{25}}}{{p^{10}x^{2}}} = \dfrac{{p^{25}}}{{p^{10}}} \cdot \dfrac{{1}}{{x^{2}}} = p^{{25} - {10}} \cdot x^{- {2}} = p^{15}x^{-2}$.